What is the history of the printed and mailed birth announcement and
where can I find samples?

This is what one site says about the history of birth announcements:
http://www.pregnancy.org/article.php?sid=2380

At one time, it was thought to be fancy to have a folding card,
decorated with a little bow in pink or blue, that included a small
visiting card with the child's name.  This harked back to the
tradition of sending cards to announce one's presence when moving to a
new town in the days before modern communication.